Deep Signature Transforms

TL;DR

This paper introduces a novel deep learning approach that integrates the signature transform as a learnable layer, enabling data-dependent feature selection and improved neural network performance.

Contribution

It proposes combining signature transforms with deep learning by learning stream augmentations and using the transform as a neural network layer, enhancing flexibility and expressiveness.

Findings

Empirical results support the theoretical advantages of the method.

The approach improves performance on sequential data tasks.

Code implementation is publicly available.

Abstract

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages of the signature transform with modern deep learning frameworks. By learning an augmentation of the stream prior to the signature transform, the terms of the signature may be selected in a data-dependent way. More generally, we describe how the signature transform may be used as a layer anywhere within a neural network. In this context it may be interpreted as a pooling operation. We present the results of empirical experiments to back up the theoretical justification. Code available at https://github.com/patrick-kidger/Deep-Signature-Transforms.